Non‐linear bending waves in Keplerian accretion discs
Non‐linear bending waves in Keplerian accretion discs
复制标题
开普勒吸积盘中的非线性弯曲波
DOI：
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
Gordon I. Ogilvie
中科院分区：
文献类型：
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作者：
Gordon I. Ogilvie
本文研究了翘曲吸积盘的非线性动力学，研究了具有可忽略粘性和自重力的薄开普勒盘的重要情况。本文正式导出了一维演化方程，该方程描述了除参数不稳定性外对弯曲波传播的主要非线性和色散影响。它具有导数非线性薛定谔方程（DNLS）的形式，其系数是针对圆盘的特定模型显式获得的。详细分析了该方程的性质，并给出了数值解法。非线性和色散效应都取决于气体通过其绝热指数Γ的可压缩性。在实际情况下，非线性导致波陡增，支持孤立波。还考虑了小的有效粘度的影响，它可以抑制参数的不稳定性。这种分析可以提供一个有用的点来比较理论和数值模拟的翘曲吸积盘。
The non-linear dynamics of a warped accretion disc is investigated in the important case of a thin Keplerian disc with negligible viscosity and self-gravity. A one-dimensional evolutionary equation is formally derived that describes the primary non-linear and dispersive effects on propagating bending waves other than parametric instabilities. It has the form of a derivative non-linear Schrodinger (DNLS) equation with coefficients that are obtained explicitly for a particular model of a disc. The properties of this equation are analysed in some detail and illustrative numerical solutions are presented. The non-linear and dispersive effects both depend on the compressibility of the gas through its adiabatic index Γ. In the physically realistic case r 3, non-linearity leads to wave steepening and solitary waves are supported. The effects of a small effective viscosity, which may suppress parametric instabilities, are also considered. This analysis may provide a useful point of comparison between theory and numerical simulations of warped accretion discs.